# Luke Alvarez

Calculus teacher | Tutor for 6 years

I hold a degree in Calculus from the Fashion Institute of Technology. My passion lies in deciphering the intricate language of numbers and functions. Through personalized tutoring sessions, I strive to demystify calculus concepts, making them accessible and engaging for students. With a deep understanding of mathematical principles and real-world applications, I empower learners to conquer challenges and unlock their full potential. Whether it's derivatives, integrals, or differential equations, I am committed to fostering a supportive learning environment where curiosity thrives and mathematical fluency flourishes. Join me on a journey of discovery and mastery in the world of calculus.

## Questions

How do you sketch the graph #y=(2e^x)/(1+e^(2x))# using the first and second derivatives?

The curve Y= X^3-3x has a slope 3 at two points. Find the two points?

How do you integrate by substitution #int u^2sqrt(u^3+2)du#?

What is #int (-3x^3+4 ) / (5x^2-2x +1 )#?

What is the antiderivative of #x/(x^2+1) #?

If #f(x) =tan^2(x/2) # and #g(x) = sqrt(5x-1 #, what is #f'(g(x)) #?

How do you find the definite integral of #sqrt(y+1)*dy# from #[-1, 0]#?

How do you differentiate #g(x)=cos(10^(2x))#?

How do you find the limit of # (1/4x + 1/x) / (4+x)# as x approaches -4?

What is the equation of the tangent line of #r=cos(theta+(5pi)/4) * sin(theta-(17pi)/12)# at #theta=(-5pi)/12#?

How do you find the derivative using limits of #f(x)=-5x#?

What is the distance between the following polar coordinates?: # (1,pi/2), (-1,pi/2) #

How do integrate #int e^(cos)(t) (sin 2t) dt# between a = 0, #b = pi#?

How do you use the integral test to determine if #1/(sqrt1(sqrt1+1))+1/(sqrt2(sqrt2+1))+1/(sqrt3(sqrt3+1))+...1/(sqrtn(sqrtn+1))+...# is convergent or divergent?

Let #y=[(x^(2x)(x-1)^3)/(3+5x)^4]#, how do you use logarithmic differentiation to find #dy/dx#?

What is the derivative of #2x(4-x^2)^(1/2)#?

For what values of x, if any, does #f(x) = 1/(x^2-4x+4) # have vertical asymptotes?

How do you determine whether the function #f(x)=x^8(ln(x))# is concave up or concave down and its intervals?

How do you differentiate #y = x^2(sinx)^4 + x(cosx)^-2#?

How do you evaluate #(sin2h*sin3h) /( h^2)# as h approaches 0?